Two Just Stop Oil protesters have denied damaging glass protecting the Rokeby Venus painting in London's National Gallery.
Harrison Donnelly, 20, of Sillitoe Way, Nottingham, and Hanan Ameur, 22, of Hornsey Road, Islington, are accused of attacking the artwork on 6 November.
The pair both pleaded not guilty to one count of causing criminal damage.
Westminster Magistrates' Court heard it will cost more than £6,000 to repair the glass.
The court heard the artwork was not thought to have been damaged.
District Judge Michael Snow granted the pair conditional bail until their pre-trial plea hearing at Southwark Crown Court on 19 December.
He banned Mr Donnelly from entering inside the M25 other than to attend court or meet his solicitors. Ms Ameur was forbidden from entering the London borough of Westminster, even just to travel through it.
Judge Snow said: "If you come back [to court] for something else I will remand you into custody.
"If you want to be inside [prison] for Christmas commit another offence and that's what's going to happen to you."